Angular closure of a seven-sided traverse against a k√n tolerance
Seven interior angles that sum 21 seconds over the geometric condition. Test the misclosure against the k√n tolerance a 10-second instrument justifies, then distribute it equally and prove the adjusted angles close.
Recall· about 18 minutes by hand· 4 steps
Given
A closed seven-sided traverse was observed with a 10″ total station, each interior angle turned by one direct and one reverse pointing and meaned.
The field specification allows an angular misclosure of k√n seconds, with k taken as the least count of the instrument, 10″, and n the number of angles.
No angle is suspected of a blunder; all were turned with the same procedure and the same care.
Required
The geometric condition the seven angles must satisfy, and the observed misclosure.
Whether the misclosure meets the tolerance.
The correction to each angle and the adjusted angles.
Work it through yourself before reading on - the solution below shows every step, so there is no way to skim it without giving the answer away.
Premium
The worked solution is part of Premium
This problem is 4 steps of computation, with the arithmetic shown at every stage and an independent check at the end. Several problems from every category are free to read in full so you can judge the format first.
Every calculator, the whole reference library and all the guides are free to use forever - the practice bank, the full problem library and the printable job paperwork are the paid upgrade.